Garden of Laplacian Borderenergetic Graphs

Let G be a graph of order n. G is said to be L-borderenergetic if its Laplacian energy is the same as the energy of the complete graph K-n, i.e. LE(G) = 2(n - 1). In this paper, we construct 36 infinite classes of L-borderenergetic graphs. The L-borderenergetic graphs we construct are composition of the complete graphs and the cycle graphs under the operators join, union and complements. They are non-complete and distinct from the previously known L-borderenergetic graphs.